In [1]:
%matplotlib inline

import pandas as pd
import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt
from matplotlib import cm

import ipyparallel as ipp

from time import time
from datetime import datetime

import motif as mf

from sklearn.model_selection import GridSearchCV, RandomizedSearchCV
from sklearn.decomposition import PCA
from sklearn.utils import shuffle
from sklearn.metrics import mean_absolute_error
from sklearn.metrics import roc_curve, roc_auc_score
from sklearn.model_selection import train_test_split, cross_val_score, cross_validate

from scipy.stats import spearmanr
from scipy.stats import pearsonr

Intel(R) Extension for Scikit-learn* enabled (https://github.com/intel/scikit-learn-intelex)
In [2]:
### set parameters for the motif analysis

PROTEIN_NAME = 'Prdm11'
PROT_CONC = 0.1  # free protein concentration at binding reation; PBM typically 0.1 and RNACompete typically 0.002
BOTH_STRANDS = True  # wheter both strands are present for binding; True if double-stranded DNA or RNA is used as probes

STAGES=mf.stage(protein=PROTEIN_NAME)
In [3]:
### read data

## RNAcompete sample data
#dfprobes_raw=pd.read_excel('./data/RNAcompete/A2BP1.xlsx')
#dfprobes_raw=pd.read_excel('./data/RNAcompete/HNRNPA1.xlsx')
#dfprobes_raw=pd.read_excel('./data/RNAcompete/PTBP1.xlsx')
#dfprobes_raw=pd.read_excel('./data/RNAcompete/RBM24.xlsx')


#dfprobes_raw=pd.read_csv('./data/samplePBMs/Mlx__pTH2882_HK.raw', sep='\t')
#dfprobes_raw=pd.read_csv('./data/samplePBMs/Klf9__pTH2353_HK.raw', sep='\t')
dfprobes_raw=pd.read_csv('./data/samplePBMs/Prdm11__pTH3455_HK.raw', sep='\t')
#dfprobes_raw=pd.read_csv('./data/samplePBMs/Sox10__pTH1729_HK.raw', sep='\t')


print('Columns of imported Data File: %s' % dfprobes_raw.columns)
#dfprobes_raw.describe()
#dfprobes_raw.info()

Columns of imported Data File: Index(['#id_spot', 'row', 'col', 'control', 'id_probe', 'pbm_sequence',
       'linker_sequence', 'mean_signal_intensity', 'mean_background_intensity',
       'flag'],
      dtype='object')
In [8]:
### select columns for probe sequence and signal

column_sequence = 'pbm_sequence'
column_signal = 'mean_signal_intensity'
background_signal = 'mean_background_intensity'  #set to None if not needed
#background_signal=None

#basic preprocessing
dfprobes_raw[column_signal] = dfprobes_raw[column_signal].apply(
    lambda a: np.NaN if a == ' ' else a)
dfprobes_raw[column_signal] = dfprobes_raw[column_signal].apply(
    lambda a: np.NaN if a == '' else a)
dfprobes_raw[column_sequence] = dfprobes_raw[column_sequence].apply(
    lambda a: np.NaN if str(a).lower() == 'nan' else a)
dfprobes_raw[column_sequence] = dfprobes_raw[column_sequence].apply(
    lambda a: np.NaN if a == '' else a)
dfprobes_raw = dfprobes_raw.dropna()

#construct new dataframe with only necessary data
if type(background_signal) == type(None):
    dfprobes = pd.DataFrame({
        'seq':
        dfprobes_raw[column_sequence].astype(str),
        'signal binding':
        dfprobes_raw[column_signal].astype(np.float32)
    })  #rebuild dataframe
else:
    dfprobes = pd.DataFrame({
        'seq':
        dfprobes_raw[column_sequence].astype(str),
        'signal':
        dfprobes_raw[column_signal].astype(np.float32),
        'background':
        dfprobes_raw[background_signal].astype(np.float32)
    })  #rebuild dataframe
    dfprobes['signal binding'] = dfprobes['signal'] - dfprobes['background']

dfprobes = dfprobes.dropna()    

    
# display main properties of data set
dfprobes['signal binding'].plot(figsize=(15, 5))
dfprobes.describe()

### check type of nucleic acid

dfprobes['seq'] = dfprobes['seq'].apply(
    lambda seq: seq.upper().replace(" ", ""))  #upper and remove blanks
dfprobes['RNA'] = dfprobes['seq'].apply(
    lambda seq: all(char in 'ACGU' for char in seq))
dfprobes['DNA'] = dfprobes['seq'].apply(
    lambda seq: all(char in 'ACGT' for char in seq))
non_RNA_counts = len(dfprobes[dfprobes['RNA'] == False])
non_DNA_counts = len(dfprobes[dfprobes['DNA'] == False])

if non_RNA_counts < non_DNA_counts:
    NUC_TYPE = 'RNA'
    print('I: RNA probes detected!')
else:
    NUC_TYPE = 'DNA'
    print('I: DNA probes detected!')

if NUC_TYPE == 'RNA' and non_RNA_counts != 0:
    print(
        'E: The probe sequences appear to be RNA, however there are some non-RNA nucleotides in the sequences.'
    )
    print('E: Please check the following sequnces %s' %
          dfprobes[dfprobes['RNA'] == False])

if NUC_TYPE == 'DNA' and non_DNA_counts != 0:
    print(
        'E: The probe sequences appear to be RNA, however there are some non-RNA nucleotides in the sequences.'
    )
    print('E: Please check the following sequnces %s' %
          dfprobes[dfprobes['DNA'] == False])

I: DNA probes detected!
In [9]:
### option to add a constant sequence at the 3' end and 5' end
sequence_to_be_added_5 = ''
sequence_to_be_added_3 = 'CCTGT'  # standard PBM arrays: CCTGTGTGAAATTGTTATCCGCTCT T7 array: GTCTTGA..
dfprobes['seq'] = sequence_to_be_added_5.upper(
) + dfprobes['seq'] + sequence_to_be_added_3.upper()
print(
    f"I: The nucleotide sequence {sequence_to_be_added_5.upper()} has been added to the 5' end all probe sequences."
)
print(
    f"I: The nucleotide sequence {sequence_to_be_added_3.upper()} has been added to the 3' end all probe sequences."
)

I: The nucleotide sequence  has been added to the 5' end all probe sequences.
I: The nucleotide sequence CCTGT has been added to the 3' end all probe sequences.
In [10]:
### egalize length
dfprobes['seq_length'] = dfprobes['seq'].apply(len)

if max(dfprobes['seq_length']) != min(dfprobes['seq_length']):
    print('I: Probes length is not uniform, detected range: %i ..%i' %
          (min(dfprobes['seq_length']), max(dfprobes['seq_length'])))
    max_length = max(dfprobes['seq_length'])
    dfprobes['padded_sequence'] = dfprobes['seq'].apply(
        lambda seq: seq + ((max_length - len(seq)) * '-'))
    print(
        "I: Probe sequences have been padded at the 5' to the uniform length of %i nucleotides"
        % max_length)
else:
    print('I: Probe sequences have the uniform length of %i nucleotides' %
          (dfprobes['seq_length'].median()))
    dfprobes['padded_sequence'] = dfprobes['seq']

print('I: Total datasets contains %i sequences.' % len(dfprobes))

# visualize composition of each position
df_nucleotides = mf.split_sequence_in_nucleotides(dfprobes['padded_sequence'])
dfcount = pd.DataFrame(index=['A', 'C', 'G', 'T', 'U', '-'])
for column in df_nucleotides:
    dfcount[column] = df_nucleotides[column].value_counts()
dfcount = dfcount.fillna(0)  #zeros for NaN
dfcount.transpose().plot(figsize=(15, 5), kind='bar')
print('I: Visualisation of the base composition per position')
print(
    'I: If positions are invariant they can be removed before sequence analysis.'
)

I: Probes length is not uniform, detected range: 36 ..40
I: Probe sequences have been padded at the 5' to the uniform length of 40 nucleotides
I: Total datasets contains 40330 sequences.
I: Visualisation of the base composition per position
I: If positions are invariant they can be removed before sequence analysis.
In [11]:
# You may remove invariant continuos positions by adjusting the slicing.
# It is recommended to leave a few invariant positions to allow for binding events
# between the variable and constant part of the probes.

dfprobes['padded_sequence'] = dfprobes['padded_sequence'].apply(lambda s: s[:40])  ### <==== do the slicing here

# visualize composition of each position
print('I: Visualisation of the base composition per position after slicing.')
df_nucleotides = mf.split_sequence_in_nucleotides(dfprobes['padded_sequence'])
dfcount = pd.DataFrame(index=['A', 'C', 'G', 'T', 'U', '-'])
for column in df_nucleotides:
    dfcount[column] = df_nucleotides[column].value_counts()
dfcount = dfcount.fillna(0)  #zeros for NaN
dfcount.transpose().plot(figsize=(15, 5), kind='bar')
plt.show()

# preparation for later classification
mean = dfprobes['signal binding'].mean()
std = dfprobes['signal binding'].std()
THRESHOLD = mean + 4 * std  #4*std used according to Weirauch et al., 2013
dfprobes['positive probe'] = dfprobes['signal binding'].apply(
    lambda s: True if s > THRESHOLD else False)

print(
    'I: The whole dataset has been used to set the threshold for a positive probe.'
)
print('I: The threshold is %f' % THRESHOLD)
print(
    f"I: {len(dfprobes[dfprobes['positive probe']])} probes of {len(dfprobes)} are above threshold."
)

if len(dfprobes[dfprobes['positive probe']]) == 0:
    print(
        'E: No probe above THRESHOLD. Classification is not possible. Please adjust the THRESHOLD.'
    )

I: Visualisation of the base composition per position after slicing.

I: The whole dataset has been used to set the threshold for a positive probe.
I: The threshold is 21424.794189
I: 577 probes of 40330 are above threshold.
In [12]:
#### Shuffle and prepare dataset for training and testing

# shuffle and split
dfprobes = shuffle(dfprobes)
dftrain, dftest = train_test_split(dfprobes, test_size=0.2)

print(
    'I: The whole dataset has been split in training (80%) and test (20%) datasets.'
)

# display histogramms of test and training set
dftrain['signal binding'].plot(kind='hist', bins=25).axvline(x=THRESHOLD, color='r', linestyle='-.', lw=0.5, label='threshold classification')
dftest['signal binding'].plot(kind='hist', bins=25)
plt.show()

# generate a subset with maximal 1000 probes

downsampled_size = 1000  # You may change downsampled size here.

percentile = 0.5 * downsampled_size / len(
    dftrain
) * 100  #percentile required for lowest and highest to achieve down-sampled size
if percentile < 4:
    percentile = 4  #do not use only the extreme values
elif percentile > 10:
    percentile = 10  #avoid taking value from the mid-range

if len(dftrain) * percentile * 2 / 100 < downsampled_size / 4:
    print('W: The subset only contains %i probes - a rather low number.' %
          dftrain * percentile * 2 / 100)

print(
    'I: A downsampled dataset containing the lowest and highest %.1f %% of the dataset is generated.'
    % percentile)
dfsubset_high = dftrain[dftrain['signal binding'] >= dftrain['signal binding'].quantile(1 - percentile / 100)]  # highest part
dfsubset_low = dftrain[dftrain['signal binding'] <= dftrain['signal binding'].quantile(percentile / 100)]  # lowest part
print('I: Median values of lowest and highest %.1f %%:  %r  %r' %
      (percentile, dfsubset_low['signal binding'].quantile(0.5),
       dfsubset_high['signal binding'].quantile(0.5)))

if len(dfsubset_high) + len(dfsubset_low) > downsampled_size:
    print('I: The dataset is further downsampled to %i sequences.' %
          downsampled_size)
    dfsubset_high = dfsubset_high.sample(downsampled_size - int(downsampled_size / 2))
    dfsubset_low = dfsubset_low.sample(int(downsampled_size / 2))
    dfsubset = pd.concat([dfsubset_high, dfsubset_low])
else:
    dfsubset = pd.concat([dfsubset_high, dfsubset_low])

dfsubset = shuffle(dfsubset)   
    
# display main properties of downsampled data set
print('I: Histogramm of the downsampled dataset along the with classification threshold.')
dfsubset['signal binding'].plot(kind='hist', bins=25).axvline(x=THRESHOLD, color='r', linestyle='-.', lw=0.5, label='threshold classification')
plt.show()

# establish numpy arrays of the sequenc and binding data in the dataframes

# complete data
X=mf.hotencode_sequence(dfprobes['padded_sequence'], nuc_type=NUC_TYPE)
y=np.array(dfprobes['signal binding'])

# training set
X_train=mf.hotencode_sequence(dftrain['padded_sequence'], nuc_type=NUC_TYPE)
y_train=np.array(dftrain['signal binding'])

# subset of training set
X_subset=mf.hotencode_sequence(dfsubset['padded_sequence'], nuc_type=NUC_TYPE)
y_subset=np.array(dfsubset['signal binding'])

# test set
X_test=mf.hotencode_sequence(dftest['padded_sequence'], nuc_type=NUC_TYPE)
y_test=np.array(dftest['signal binding'])

I: The whole dataset has been split in training (80%) and test (20%) datasets.

I: A downsampled dataset containing the lowest and highest 4.0 % of the dataset is generated.
I: Median values of lowest and highest 4.0 %:  274.64227294921875  18740.26171875
I: The dataset is further downsampled to 1000 sequences.
I: Histogramm of the downsampled dataset along the with classification threshold.
In [13]:
### perform a quick & dirty round for a short motif by fitting on subset to check data integrity

#fit regression quick_model
quick_model=mf.findmotif(motif_length=3, protein_conc=PROT_CONC, both_strands=BOTH_STRANDS, ftol=0.01)

start = time()
quick_model.fit(X_subset,y_subset)
print("I: Optimization took %.2f hours." % ((time() - start)/3600))

# print & display main results
quick_model.analyse_motif(X_subset,y_subset, THRESHOLD, nuc_type=NUC_TYPE)

# store results and display stages
STAGES.append('quick', quick_model)
mf.display_df(STAGES.df, nuc_type=NUC_TYPE)

I: Optimization took 0.03 hours.
I: energy matrix and logos:


        A      C     G     T
0 -15088  16607  2650 -4169
1 -13696  17505 -4679   871
2   2089    451  3897 -6439

I: summed absolute energies of each position:
0    38516
1    36753
2    12878
dtype: int64

I: averaged summed energy over all positions: 29382
I: Mean and Standard Deviation for the Free Energy G to all subsequences of all probes: -3622 +/- 17452
I: Plot of the Occupancy of a subsite as the function of the Free Energy G 
   overlaid with the distribution of the Free Energy of all subsites.
I: There shall be only a small overlap of both curves. i.e. only the most negative Free Energies
    lead to a measurable occupancy.

I: Calculated occupancy over all subsite of a single probe:
   binding:  0.02670 .. 7.04804 (ratio: 263.9)
I: number of probes: 1000
I: Pearson Correlation  r: 0.4515
I: mean absolute error: 8380.6232

I: Classification performance AUROC: 0.7091
stage protein # probes motif length r AUROC G0 G0 fitted ratio max binding min binding energies model logo
0 quick Prdm11 1000 3 0.45148 0.709106 -11473.366709 False 263.932317 7.048041 0.026704 -15088,.. suppressed
In [14]:
#### Perfrom GridCV Search for exploration of the motif length goal: identify the minimum motif length which gives a good r-value

# optional: allow for global optimization to verify whether the local optimization is good enough
# not recommended include fitG0=True. This option should only be considered when the local optimization is started with an approximate motif and the start parameter is set
# not recommended set time_dissociation. The effect of dissociation should be only considered when the local optimization is started with an approximate motif.


# prepare grid search over motif_length
model_grid=mf.findmotif(protein_conc=PROT_CONC, both_strands=BOTH_STRANDS)
param_grid = {"motif_length": [3,4,5,6,7,8]}     # choose sensible range for length of motif

# define custom refit function
def custom_refit(cv_results):
    """returns index of max r2/sqrt(motif_length)"""
    df_grid=pd.DataFrame(cv_results)
    index=(df_grid['mean_test_score']/(df_grid['param_motif_length'].apply(float).apply(np.sqrt))).idxmax()
    return index

# run grid search and refit according to custom refit
grid_search = GridSearchCV(model_grid, param_grid=param_grid, verbose=2, cv=5, refit=custom_refit, n_jobs=-1)

start = time()
grid_search.fit(X_subset, y_subset)

print("I: GridSearchCV took %.2f hours for %d candidate parameter settings."
    % ((time() - start)/3600, len(grid_search.cv_results_["params"])))
print('I: number of samples: %i' %len(X_subset))

df_grid=pd.DataFrame(grid_search.cv_results_)
print('I: Plot of r2 vs motif length and vs root(motif length)')
df_grid.rename(columns={'mean_test_score':'r2'}, inplace=True)
df_grid.plot(kind='scatter', x='param_motif_length', y='r2', yerr='std_test_score', figsize=(5,3)).set_xticks(param_grid["motif_length"])
df_grid['r2/sqrt(length)']=df_grid['r2']/(df_grid['param_motif_length'].apply(float).apply(np.sqrt))
df_grid['std/sqrt(length)']=df_grid['std_test_score']/(df_grid['param_motif_length'].apply(float).apply(np.sqrt))
df_grid.plot(kind='scatter', x='param_motif_length', y='r2/sqrt(length)',yerr='std/sqrt(length)', figsize=(5,3)).set_xticks(param_grid["motif_length"])
plt.show()

best_index=df_grid['r2/sqrt(length)'].idxmax()
CORE_MOTIF_LENGTH=df_grid.loc[best_index, 'param_motif_length']
print(f'I: The maximum ({CORE_MOTIF_LENGTH}) is suggested as CORE_MOTIF_LENGTH')

print('I: motif obtained with the best estimator from gridCV search')
# print & display results from best estimator
model_grid=grid_search.best_estimator_
model_grid.analyse_motif(X_subset,y_subset, THRESHOLD, nuc_type=NUC_TYPE)

# store results and display stages
STAGES.append('best grid', model_grid)
mf.display_df(STAGES.df, nuc_type=NUC_TYPE)

Fitting 5 folds for each of 6 candidates, totalling 30 fits
I: GridSearchCV took 1.73 hours for 6 candidate parameter settings.
I: number of samples: 1000
I: Plot of r2 vs motif length and vs root(motif length)

I: The maximum (7) is suggested as CORE_MOTIF_LENGTH
I: motif obtained with the best estimator from gridCV search
I: energy matrix and logos:


        A      C     G     T
0    800    -93   612 -1319
1  11667  -4359  -551 -6756
2   -201   4515 -7675  3361
3    863 -10062  7674  1524
4   7049   1842 -4842 -4049
5   -389   1057  -924   256
6   -411    509   -31   -67

I: summed absolute energies of each position:
0     2825
1    23334
2    15753
3    20124
4    17784
5     2628
6     1019
dtype: int64

I: averaged summed energy over all positions: 11924
I: Mean and Standard Deviation for the Free Energy G to all subsequences of all probes: -366 +/- 11472
I: Plot of the Occupancy of a subsite as the function of the Free Energy G 
   overlaid with the distribution of the Free Energy of all subsites.
I: There shall be only a small overlap of both curves. i.e. only the most negative Free Energies
    lead to a measurable occupancy.

I: Calculated occupancy over all subsite of a single probe:
   binding:  0.00024 .. 0.06713 (ratio: 278.9)
I: number of probes: 1000
I: Pearson Correlation  r: 0.7874
I: mean absolute error: 5048.1652

I: Classification performance AUROC: 0.8663
stage protein # probes motif length r AUROC G0 G0 fitted ratio max binding min binding energies model logo
0 quick Prdm11 1000 3 0.451480 0.709106 -11473.366709 False 263.932317 7.048041 0.026704 -15088,.. suppressed
1 best grid Prdm11 1000 7 0.787405 0.866291 659.713619 False 278.858237 0.067129 0.000241 800,.. suppressed
In [15]:
### run a number of identical optimizations with motif length found during grid search
### goal: find best motif through repetition, judge stabiltiy of optimization

#CORE_MOTIF_LENGTH=5  # adjust core motif length if needed, motif length can be changed later

# prepare for ipyparallel
number_of_optimizations = 20
model_list = [mf.findmotif(motif_length=CORE_MOTIF_LENGTH, protein_conc=PROT_CONC, both_strands=BOTH_STRANDS)] * number_of_optimizations
X_list = [X_subset] * number_of_optimizations
y_list = [y_subset] * number_of_optimizations


def single_job(model, X, y):
    model.fit(X, y)
    return {'model':model}

# run the optimizations on ipp.cluster
start = time()
with ipp.Cluster(log_level=40) as rc:
    rc[:].use_pickle()
    view = rc.load_balanced_view()
    asyncresult = view.map_async(single_job, model_list, X_list, y_list)
    asyncresult.wait_interactive()
    result = asyncresult.get()
print("I: Optimization took %.2f hours." % ((time() - start) / 3600))


  
# assemble results and analyze
df_repetitions=pd.DataFrame(result)
df_repetitions['r (subset)']=df_repetitions['model'].apply(lambda e: e.rvalue)
df_repetitions['r (train)']=df_repetitions['model'].apply(lambda e: mf.linregress(e.predict(X_train),y_train).rvalue)
df_repetitions['r (test)']=df_repetitions['model'].apply(lambda e: mf.linregress(e.predict(X_test),y_test).rvalue)
df_repetitions['G0']=df_repetitions['model'].apply(lambda e: e.finalG0_)
df_repetitions['max binding']=df_repetitions['model'].apply(lambda e: e.max_binding_fit)
df_repetitions['min binding']=df_repetitions['model'].apply(lambda e: e.min_binding_fit)
df_repetitions['ratio'] = df_repetitions['model'].apply(lambda e: e.ratio)
df_repetitions['energies']=df_repetitions['model'].apply(lambda e: e.energies_)
#df_repetitions['information']=df_repetitions['model'].apply(lambda e: mf.energies2information(e.energies_))


# display results of the ensemble of optimizations
print('I: Results of the repeated motif finding, sorted according to the regression coefficient with the train dataset')
df_repetitions.sort_values('r (train)', ascending=False, inplace=True)
mf.display_df(df_repetitions, nuc_type=NUC_TYPE)

  0%|          | 0/16 [00:00<?, ?engine/s]
single_job:   0%|          | 0/20 [00:00<?, ?tasks/s]
I: Optimization took 1.06 hours.
I: Results of the repeated motif finding, sorted according to the regression coefficient with the train dataset
model r (subset) r (train) r (test) G0 max binding min binding ratio energies logo
4 suppressed 0.864080 0.735176 0.750976 659.713619 1.584724 0.000686 2311.633856 1549,..
14 suppressed 0.845226 0.700097 0.711644 659.713619 1.904420 0.001625 1172.024097 -346,..
12 suppressed 0.832139 0.683201 0.709216 659.713619 1.301013 0.004848 268.369575 254,..
5 suppressed 0.815892 0.668539 0.685388 659.713619 1.951732 0.002082 937.220458 -370,..
15 suppressed 0.789596 0.663934 0.672350 659.713619 0.847323 0.001453 583.180074 -598,..
19 suppressed 0.776544 0.643679 0.657670 659.713619 1.598532 0.000706 2265.225137 1394,..
0 suppressed 0.776935 0.642115 0.655973 659.713619 1.430209 0.001257 1137.665142 1364,..
3 suppressed 0.776369 0.640203 0.654302 659.713619 1.539078 0.000633 2430.269794 1359,..
1 suppressed 0.804165 0.624703 0.639571 659.713619 2.239245 0.001305 1715.322556 -2934,..
18 suppressed 0.788495 0.552055 0.574082 659.713619 0.086391 0.000143 605.063824 850,..
11 suppressed 0.735823 0.545395 0.561459 659.713619 1.523597 0.000433 3515.846531 -596,..
10 suppressed 0.796310 0.528959 0.539938 659.713619 6.828242 0.004917 1388.811238 -2255,..
6 suppressed 0.796906 0.528956 0.541552 659.713619 6.788038 0.005682 1194.629692 -1766,..
8 suppressed 0.792411 0.527226 0.539990 659.713619 6.551525 0.009889 662.525950 -1622,..
2 suppressed 0.791989 0.527052 0.540168 659.713619 6.598215 0.010918 604.360223 -1510,..
13 suppressed 0.801362 0.519204 0.524001 659.713619 6.006226 0.003799 1580.821551 -2664,..
16 suppressed 0.801276 0.518778 0.523467 659.713619 6.129605 0.004447 1378.364083 2364,..
7 suppressed 0.800254 0.517025 0.522122 659.713619 6.289050 0.006601 952.737902 -2840,..
9 suppressed 0.784569 0.516322 0.531929 659.713619 5.701631 0.000960 5940.021764 -2382,..
17 suppressed 0.678227 0.321258 0.333524 659.713619 2.524110 0.001758 1436.179283 -189,..
In [16]:
### compare energy matrices of ensemble using PCA
print('I: Histogram of the regression coefficients r obtained by repeated optimizaion with the subset.')
df_repetitions['r (subset)'].plot(kind='hist')
plt.show()

pca = PCA(n_components=2)
pca_2c=pca.fit_transform(df_repetitions['energies'].tolist())    
df_repetitions[['PCA1', 'PCA2']]=pca_2c

if sum(pca.explained_variance_ratio_)<0.5:
      print('W: 2-dimensional PCA explained only %i %% of variance' %(sum(pca.explained_variance_ratio_)*100))
else:
    print('I: 2-dimensional PCA explained %i %% of variance.' %(sum(pca.explained_variance_ratio_)*100))
print('I: Visualization of the PCA with the regression quality vs. subset and training dataset by color.')        
df_repetitions.plot(x='PCA1', y='PCA2', kind='scatter', c='r (subset)',cmap=cm.coolwarm, edgecolors='black', linewidths=0.3)
df_repetitions.plot(x='PCA1', y='PCA2', kind='scatter', c='r (train)',cmap=cm.coolwarm, edgecolors='black', linewidths=0.3)

I: Histogram of the regression coefficients r obtained by repeated optimizaion with the subset.

I: 2-dimensional PCA explained 52 % of variance.
I: Visualization of the PCA with the regression quality vs. subset and training dataset by color.

/home/GLipps/.local/lib/python3.8/site-packages/sklearn/utils/deprecation.py:101: FutureWarning: Attribute `n_features_` was deprecated in version 1.2 and will be removed in 1.4. Use `n_features_in_` instead.
  warnings.warn(msg, category=FutureWarning)
Out[16]:
<matplotlib.axes._subplots.AxesSubplot at 0x7f1c06486190>
In [17]:
# visualisation of the motif with the highest r with the train dataset
print('I: Best motif according to r (train) from the repeated optimizations.')
print('I: PCA components: %i, %i' %(df_repetitions.iloc[0]['PCA1'], df_repetitions.iloc[0]['PCA2']))
model_best_repetition=df_repetitions.iloc[0]['model']
model_best_repetition.analyse_motif(X_subset,y_subset, THRESHOLD, nuc_type=NUC_TYPE) 
# store results and display stages
STAGES.append('best repetition', model_best_repetition, new_entries={'r (test)': mf.linregress(model_best_repetition.predict(X_test),y_test).rvalue})
mf.display_df(STAGES.df, nuc_type=NUC_TYPE)

I: Best motif according to r (train) from the repeated optimizations.
I: PCA components: -9090, 21037
I: energy matrix and logos:


       A      C      G     T
0  1549    499    506 -2556
1 -3841   3140   6635 -5935
2 -9020  17513 -16771  8278
3 -1987 -10081   7303  4765
4  2435   2686  -5412   290
5    71   1390  -1892   430
6  -430    485   -410   355

I: summed absolute energies of each position:
0     5113
1    19553
2    51583
3    24138
4    10825
5     3785
6     1681
dtype: int64

I: averaged summed energy over all positions: 16668
I: Mean and Standard Deviation for the Free Energy G to all subsequences of all probes: 423 +/- 16245
I: Plot of the Occupancy of a subsite as the function of the Free Energy G 
   overlaid with the distribution of the Free Energy of all subsites.
I: There shall be only a small overlap of both curves. i.e. only the most negative Free Energies
    lead to a measurable occupancy.

I: Calculated occupancy over all subsite of a single probe:
   binding:  0.00069 .. 1.58472 (ratio: 2311.6)
I: number of probes: 1000
I: Pearson Correlation  r: 0.8641
I: mean absolute error: 3694.2461

I: Classification performance AUROC: 0.8802
stage protein # probes motif length r AUROC G0 G0 fitted ratio max binding min binding energies model logo r (test)
0 quick Prdm11 1000 3 0.451480 0.709106 -11473.366709 False 263.932317 7.048041 0.026704 -15088,.. suppressed NaN
1 best grid Prdm11 1000 7 0.787405 0.866291 659.713619 False 278.858237 0.067129 0.000241 800,.. suppressed NaN
2 best repetition Prdm11 1000 7 0.864080 0.880196 659.713619 False 2311.633856 1.584724 0.000686 1549,.. suppressed 0.750976
In [18]:
### motif finding on complete training dataset starting with best motif from repetitions

#fit & predict optimization starting with previous energy matrix
model_train=mf.findmotif(motif_length=CORE_MOTIF_LENGTH, protein_conc=PROT_CONC, both_strands=BOTH_STRANDS,
                   start=model_best_repetition.energies_)
start = time()
model_train.fit(X_train,y_train)
print("I: Optimization took %.2f hours." % ((time() - start)/3600))

# print & display main results
model_train.analyse_motif(X_train,y_train, THRESHOLD, nuc_type=NUC_TYPE)

# store results and display stages
STAGES.append('train dataset', model_train, new_entries={'r (test)': mf.linregress(model_train.predict(X_test),y_test).rvalue})
mf.display_df(STAGES.df, nuc_type=NUC_TYPE)

I: Optimization took 6.12 hours.
I: energy matrix and logos:


       A      C      G     T
0  1225    423   1155 -2804
1 -3315   3111   6151 -5948
2  8010   5503 -12981  -532
3  2591 -10243   5845  1807
4  3014   3782  -7077   281
5   751   1030  -2495   713
6 -1016    920   -430   526

I: summed absolute energies of each position:
0     5608
1    18527
2    27027
3    20486
4    14155
5     4990
6     2894
dtype: int64

I: averaged summed energy over all positions: 13384
I: Mean and Standard Deviation for the Free Energy G to all subsequences of all probes: 319 +/- 12152
I: Plot of the Occupancy of a subsite as the function of the Free Energy G 
   overlaid with the distribution of the Free Energy of all subsites.
I: There shall be only a small overlap of both curves. i.e. only the most negative Free Energies
    lead to a measurable occupancy.

I: Calculated occupancy over all subsite of a single probe:
   binding:  0.00007 .. 1.39310 (ratio: 21199.9)
I: number of probes: 32264
I: Pearson Correlation  r: 0.7735
I: mean absolute error: 1457.8057

I: Classification performance AUROC: 0.9699
stage protein # probes motif length r AUROC G0 G0 fitted ratio max binding min binding energies model logo r (test)
0 quick Prdm11 1000 3 0.451480 0.709106 -11473.366709 False 263.932317 7.048041 0.026704 -15088,.. suppressed NaN
1 best grid Prdm11 1000 7 0.787405 0.866291 659.713619 False 278.858237 0.067129 0.000241 800,.. suppressed NaN
2 best repetition Prdm11 1000 7 0.864080 0.880196 659.713619 False 2311.633856 1.584724 0.000686 1549,.. suppressed 0.750976
3 train dataset Prdm11 32264 7 0.773544 0.969873 659.713619 False 21199.906795 1.393098 0.000066 1225,.. suppressed 0.785906
In [19]:
### Based on the motif of CORE_MOTIF_LENGTH analyze the neigbouring positions 
### whether their inclusion can improve the quality of the motif
df_positions=model_train.investigate_extension_parallel(X_train,y_train, end5=3, end3=3, nuc_type=NUC_TYPE)

list_positions=df_positions.index[df_positions['+2%']].tolist()+[0] # list of positions with an increase of2% and default position 0
ext5=-min(list_positions)
ext3=max(list_positions)
print("I: It is suggested to extend the core motif at the 5' end by %i and at the 3' end by %i positions." %(ext5, ext3))

### Analyze model whether the estimated G0 is correct
df_G0=model_train.investigate_G0(X_train,y_train)

  0%|          | 0/6 [00:00<?, ?engine/s]
job5:   0%|          | 0/3 [00:00<?, ?tasks/s]
job3:   0%|          | 0/3 [00:00<?, ?tasks/s]
I: Optimization took 0.46 hours.

I: It is suggested to extend the core motif at the 5' end by 1 and at the 3' end by 0 positions.
I: Current G0 = 660 J/mol (see red broken line in figure below) with r = 0.774.
I: Maximal r is 0.774 at G0=660 J/mol (see green broken line below).
I: Maximal occupancy of 2 is reached at G0=-1340 J/mol (see blue broken line below).
I: Maximal occupancy of 0.2 is reached at G0=7660 J/mol (see blue broken line below).

I: G0 is in a range leading to maximal probe occupancy between 0.2 and 2. Good.
I: Current G0 is close to the G0 leading to maximal r. Good.
In [20]:
### fit & predict optimization starting with extended energy matrix if extension appears to improve prediction

if ext5+ext3!=0: #extension suggestion from previous analysis of the bordering positions
    expanded_energies=model_train.energies_
    # append energies of single-optimized bordering positions to energies of central part
    if ext5!=0:
        energies_5=np.concatenate(df_positions['energies'][(df_positions.index<0) & (df_positions.index>=-ext5)].to_numpy())
        expanded_energies=np.concatenate((energies_5, expanded_energies))
    if ext3!=0:
        energies_3=np.concatenate(df_positions['energies'][(df_positions.index<=ext3) & (df_positions.index>0)].to_numpy().flatten())
        expanded_energies=np.concatenate((expanded_energies,  energies_3))

    mf.energies2logo(expanded_energies, nuc_type=NUC_TYPE)
    print('I: Optimization started with extended motif.')
    expanded_motif_length=len(expanded_energies)//4
    
    
    model_extended=mf.findmotif(motif_length=expanded_motif_length, protein_conc=PROT_CONC, both_strands=BOTH_STRANDS,
                   start=expanded_energies)

    start = time()
    model_extended.fit(X_train,y_train)
    print("Optimization took %.2f hours." % ((time() - start)/3600))

    # print & display main results
    model_extended.analyse_motif(X_train,y_train, THRESHOLD, nuc_type=NUC_TYPE)

    # store results and display stages
    STAGES.append('train, extended', model_extended, new_entries={'r (test)': mf.linregress(model_extended.predict(X_test),y_test).rvalue})
    mf.display_df(STAGES.df, nuc_type=NUC_TYPE)
else:
    model_extended=model_train
    print('I: Motif is not extended based on previous analysis.')

I: Optimization started with extended motif.
Optimization took 3.39 hours.
I: energy matrix and logos:


        A      C      G     T
0  -1340   1561   1028 -1249
1   1290    360   1170 -2821
2  -3525   3436   6130 -6041
3  12320   5426 -14417 -3329
4   2548 -10320   5588  2183
5   3261   3874  -6991  -144
6    739    939  -2334   655
7   -936    821   -441   556

I: summed absolute energies of each position:
0     5180
1     5642
2    19134
3    35493
4    20640
5    14271
6     4669
7     2756
dtype: int64

I: averaged summed energy over all positions: 13473
I: Mean and Standard Deviation for the Free Energy G to all subsequences of all probes: 1318 +/- 13681
I: Plot of the Occupancy of a subsite as the function of the Free Energy G 
   overlaid with the distribution of the Free Energy of all subsites.
I: There shall be only a small overlap of both curves. i.e. only the most negative Free Energies
    lead to a measurable occupancy.

I: Calculated occupancy over all subsite of a single probe:
   binding:  0.00006 .. 1.03977 (ratio: 18179.7)
I: number of probes: 32264
I: Pearson Correlation  r: 0.8306
I: mean absolute error: 1290.2072

I: Classification performance AUROC: 0.9810
stage protein # probes motif length r AUROC G0 G0 fitted ratio max binding min binding energies model logo r (test)
0 quick Prdm11 1000 3 0.451480 0.709106 -11473.366709 False 263.932317 7.048041 0.026704 -15088,.. suppressed NaN
1 best grid Prdm11 1000 7 0.787405 0.866291 659.713619 False 278.858237 0.067129 0.000241 800,.. suppressed NaN
2 best repetition Prdm11 1000 7 0.864080 0.880196 659.713619 False 2311.633856 1.584724 0.000686 1549,.. suppressed 0.750976
3 train dataset Prdm11 32264 7 0.773544 0.969873 659.713619 False 21199.906795 1.393098 0.000066 1225,.. suppressed 0.785906
4 train, extended Prdm11 32264 8 0.830646 0.981031 3085.476013 False 18179.681260 1.039771 0.000057 -1340,.. suppressed 0.836737
In [21]:
### fit & predict optimization starting with extended energy matrix plus one bordering position on each side if current bordering position exceed the information of 0.25

I_5=mf.energies2information(model_extended.energies_[0:4])>=0.25 #sufficient information content of 5' end position
I_3=mf.energies2information(model_extended.energies_[-4:])>=0.25 #sufficient information content of 3' end position

if I_5 or I_3:
    print('I: At least one of the bordering positions has an information content of at least 0.25. Extending.')
    expanded_energies_with_border=mf.modify_energies(model_extended.energies_, end5=I_5, end3=I_3)  
    mf.energies2logo(expanded_energies_with_border, nuc_type=NUC_TYPE)
    motif_length_with_border=len(expanded_energies_with_border)//4

    model_with_border=mf.findmotif(motif_length=motif_length_with_border, protein_conc=PROT_CONC, both_strands=BOTH_STRANDS,
                   start=expanded_energies_with_border)


    start = time()
    model_with_border.fit(X_train,y_train)
    print("Optimization took %.2f hours." % ((time() - start)/3600))

    # print & display main results
    model_with_border.analyse_motif(X_train,y_train, THRESHOLD, nuc_type=NUC_TYPE)

    # store results and display stages
    STAGES.append('train, expanded, border', model_with_border, new_entries={'r (test)': mf.linregress(model_with_border.predict(X_test),y_test).rvalue})
    mf.display_df(STAGES.df, nuc_type=NUC_TYPE)
else:
    print('I: Both bordering positions of the found motif have an information content below 0.25. No futher optimization required.')

I: Both bordering positions of the found motif have an information content below 0.25. No futher optimization required.
In [23]:
STAGES.df.to_json('%s_%s-%s-%s_%s-%s.json' %(PROTEIN_NAME, datetime.now().year, datetime.now().month,datetime.now().day , datetime.now().hour, datetime.now().minute))
STAGES.df.to_pickle('%s_%s-%s-%s_%s-%s.pkl' %(PROTEIN_NAME, datetime.now().year, datetime.now().month,datetime.now().day , datetime.now().hour, datetime.now().minute))
In [ ]:
### Analyze model whether the estimated G0 is correct FIXME
df_G0=model_extended.investigate_G0(X_train,y_train)
In [ ]:
mf.energies2logo(mf.reverse_complement(STAGES.df.at[3,'energies']), nuc_type=NUC_TYPE)
In [ ]:
"""
expanded_energies=mf.modify_energies(model_train.energies_, end5=ext5, end3=ext3)  # <==== adjust end5 and end3 to enlarge core motif on 5' and 3' end
mf.energies2logo(expanded_energies, nuc_type=NUC_TYPE)
expanded_motif_length=len(expanded_energies)//4
"""
In [ ]:
df_stages.drop(index='best grid fitG0=True', inplace=True)
In [ ]:
import importlib
In [ ]:
importlib.reload(mf)
In [ ]:
start = time()
model_mae=model_with_border.refit_mae(X,y)
print("Optimization took %.2f hours." % ((time() - start)/3600))

# print & display main results
model_mae.analyse_motif(X_train,y_train, THRESHOLD, nuc_type=NUC_TYPE)

# store results and display stages
STAGES.append('train, expanded, border, mae', model_mae, new_entries={'r (test)': mf.linregress(model_mae.predict(X_test),y_test).rvalue})
mf.display_df(STAGES.df, nuc_type=NUC_TYPE)
In [ ]: